7. Roots and Radical Expressions

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7. Roots and Radical Expressions
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In this chapter, you will learn

• What a polynomial is
• Add/subtract/multiply/divide polynomials
• Simplify radicals, exponents
• Solving equations with exponents and radicals
• Complex numbers
• Conjugates

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What is a monomial?
An expression that is a number, that may or may
not include a variable.
MONOMIALS
NOT MONOMIALS
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Real Roots

• Real roots are the possible solutions to a
  number, raised to a power.

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Vocabulary and Properties
Radical sign
index
radicand
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How to find the root (other than a square root),
using a graphing calculator

• 1. Input the root you are going to take (for
  example, if you are taking the third root of a
  number, start with the 3).
• 2. Press MATH and select option 5
• 3. Enter the value you are taking the root of.
• Ex

4 MATH 5 81 ENTER
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Practice Find each root
Solutions 22, 7, and ERR NONREAL ANS
Lets take a closer look at this answer
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Properties and Notation
Why? We want to make sure that the root is always
positive when the index is an even number
When n is an even number
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Note Absolute value symbols ensure that the root
is positive when x is negative. They are not
needed for y because y2 is never negative.
Notice that the index is an odd number here . . .
Absolute value symbols must not be used here. If
x is negative, then the radicand is negative and
the root must also be negative.
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Lets try some
Simplify each expression. Use the absolute value
symbols when needed.
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Solutions
Simplify each expression. Use the absolute value
symbols when needed.
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• Properties of Exponents lets review . . .

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NEGATIVE EXPONENTRULE
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PRODUCT OR POWERRULE
HAVE TO HAVE THESAME BASE
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QUOTIENT OF POWERRULE
HAVE TO HAVE THESAME BASE
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POWER OF POWERRULE
(x4)³
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POWER OF PRODUCTRULE
(2x4)5
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POWER OF A QUOTIENTRULE
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POWER OF QUOTIENT 2RULE
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Fractional Exponents (Powers and Roots)
Power
Root
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RADICAL TO EXPONENTRULE
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RATIONAL EXPONENTRULE